41-54 Find the absolute maximum and absolute minimum values of f on the given interval. 41. f(x) = 12 + 4x − x², [0, 5] 42. f(x) = 5 + 54x − 2x³, [0, 4] 43. f(x) = 2x³ − 3x² − 12x + 1, [−2,3] 44. f(x) = x³ − 6x² + 9x + 2, [−1,4] - 45. f(x) = xª − 2x² + 3, [−2, 3] - 46. f(x) = (x² - - 47. f(t) = t√√4-t², t. 48. f(x) 1)³, [1,2] [1,2] = 2 x² 4 x² + 4² , x218ر [-4, 4] [-1,4] 49. f(x) = xe 50. f(x) = x - Inx,[¹,2] 51. f(x) = ln(x² + x + 1), [−1, 1] 52. f(x) = x − 2 tan ¹x, [0, 4] - 53. f(t) = 2 cos t + sin 2t, [0, π/2] 54. f(t) = t + cot (t/2), [π/4, 7π/4]
41-54 Find the absolute maximum and absolute minimum values of f on the given interval. 41. f(x) = 12 + 4x − x², [0, 5] 42. f(x) = 5 + 54x − 2x³, [0, 4] 43. f(x) = 2x³ − 3x² − 12x + 1, [−2,3] 44. f(x) = x³ − 6x² + 9x + 2, [−1,4] - 45. f(x) = xª − 2x² + 3, [−2, 3] - 46. f(x) = (x² - - 47. f(t) = t√√4-t², t. 48. f(x) 1)³, [1,2] [1,2] = 2 x² 4 x² + 4² , x218ر [-4, 4] [-1,4] 49. f(x) = xe 50. f(x) = x - Inx,[¹,2] 51. f(x) = ln(x² + x + 1), [−1, 1] 52. f(x) = x − 2 tan ¹x, [0, 4] - 53. f(t) = 2 cos t + sin 2t, [0, π/2] 54. f(t) = t + cot (t/2), [π/4, 7π/4]
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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#45 and #51 please
![**Exercises 41–54: Absolute Maximum and Minimum Values**
Find the absolute maximum and absolute minimum values of \( f \) on the given interval.
41. \( f(x) = 12 + 4x - x^2 \), \([0, 5]\)
42. \( f(x) = 5 + 54x - 2x^3 \), \([0, 4]\)
43. \( f(x) = 2x^3 - 3x^2 - 12x + 1 \), \([-2, 3]\)
44. \( f(x) = x^3 - 6x^2 + 9x + 2 \), \([-1, 4]\)
45. \( f(x) = x^4 - 2x^2 + 3 \), \([-2, 3]\)
46. \( f(x) = (x^2 - 1)^3 \), \([-1, 2]\)
47. \( f(t) = t \sqrt{4 - t^2} \), \([-1, 2]\)
48. \( f(x) = \frac{x^2 - 4}{x^2 + 4} \), \([-4, 4]\)
49. \( f(x) = xe^{-x^2/8} \), \([-1, 4]\)
50. \( f(x) = x - \ln x \), \([\frac{1}{2}, 2]\)
51. \( f(x) = \ln(x^2 + x + 1) \), \([-1, 1]\)
52. \( f(x) = x - 2 \tan^{-1} x \), \([0, 4]\)
53. \( f(t) = 2 \cos t + \sin 2t \), \([0, \frac{\pi}{2}]\)
54. \( f(t) = t + \cot(t/2) \), \([\frac{\pi}{4}, \frac{7\pi}{4}]\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc87785b0-7b08-4187-be5d-f53b11d0a1a0%2Fe1ec123f-f808-4ae9-a1cb-5423c430a102%2F9p9ogqw_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercises 41–54: Absolute Maximum and Minimum Values**
Find the absolute maximum and absolute minimum values of \( f \) on the given interval.
41. \( f(x) = 12 + 4x - x^2 \), \([0, 5]\)
42. \( f(x) = 5 + 54x - 2x^3 \), \([0, 4]\)
43. \( f(x) = 2x^3 - 3x^2 - 12x + 1 \), \([-2, 3]\)
44. \( f(x) = x^3 - 6x^2 + 9x + 2 \), \([-1, 4]\)
45. \( f(x) = x^4 - 2x^2 + 3 \), \([-2, 3]\)
46. \( f(x) = (x^2 - 1)^3 \), \([-1, 2]\)
47. \( f(t) = t \sqrt{4 - t^2} \), \([-1, 2]\)
48. \( f(x) = \frac{x^2 - 4}{x^2 + 4} \), \([-4, 4]\)
49. \( f(x) = xe^{-x^2/8} \), \([-1, 4]\)
50. \( f(x) = x - \ln x \), \([\frac{1}{2}, 2]\)
51. \( f(x) = \ln(x^2 + x + 1) \), \([-1, 1]\)
52. \( f(x) = x - 2 \tan^{-1} x \), \([0, 4]\)
53. \( f(t) = 2 \cos t + \sin 2t \), \([0, \frac{\pi}{2}]\)
54. \( f(t) = t + \cot(t/2) \), \([\frac{\pi}{4}, \frac{7\pi}{4}]\)
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